### Abstract

Original language | English |
---|---|

Pages (from-to) | 287-294 |

Number of pages | 7 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 39 |

Issue number | 3 |

DOIs | |

Publication status | Published - 8 May 1992 |

### Fingerprint

### Keywords

- Cubic polynomial
- Hermite
- interpolation
- monotonicity
- initial-value problem
- numerical mathematics

### Cite this

*Journal of Computational and Applied Mathematics*,

*39*(3), 287-294. https://doi.org/10.1016/0377-0427(92)90205-C

}

*Journal of Computational and Applied Mathematics*, vol. 39, no. 3, pp. 287-294. https://doi.org/10.1016/0377-0427(92)90205-C

**Monotonic piecewise cubic interpolation, with applications to ODE plotting.** / Higham, D.J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Monotonic piecewise cubic interpolation, with applications to ODE plotting

AU - Higham, D.J.

PY - 1992/5/8

Y1 - 1992/5/8

N2 - Given a set of solution and derivative values, we examine the problem of constructing a piecewise cubic interpolant which reflects the monotonicity present in the data. Drawing on the theory of Fritsch and Carlson (1980), we derive a simple algorithm that, if necessary, adds one or two extra knots between existing knots in order to preserve monotonicity. The new algorithm is completely local in nature and does not perturb the input data. We show that the algorithm is particularly suited to the case where the data arises from the discrete approximate solution of an ODE.

AB - Given a set of solution and derivative values, we examine the problem of constructing a piecewise cubic interpolant which reflects the monotonicity present in the data. Drawing on the theory of Fritsch and Carlson (1980), we derive a simple algorithm that, if necessary, adds one or two extra knots between existing knots in order to preserve monotonicity. The new algorithm is completely local in nature and does not perturb the input data. We show that the algorithm is particularly suited to the case where the data arises from the discrete approximate solution of an ODE.

KW - Cubic polynomial

KW - Hermite

KW - interpolation

KW - monotonicity

KW - initial-value problem

KW - numerical mathematics

UR - http://dx.doi.org/10.1016/0377-0427(92)90205-C

U2 - 10.1016/0377-0427(92)90205-C

DO - 10.1016/0377-0427(92)90205-C

M3 - Article

VL - 39

SP - 287

EP - 294

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 3

ER -